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                <h1 id="bootstrapped-dqn">Bootstrapped DQN</h1>
<p><strong>Actions space:</strong> Discrete</p>
<p><strong>References:</strong> <a href="https://arxiv.org/abs/1602.04621">Deep Exploration via Bootstrapped DQN</a></p>
<h2 id="network-structure">Network Structure</h2>
<p style="text-align: center;">

<img src="..\..\design_imgs\bs_dqn.png">

</p>

<h2 id="algorithm-description">Algorithm Description</h2>
<h3 id="choosing-an-action">Choosing an action</h3>
<p>The current states are used as the input to the network. The network contains several <script type="math/tex">Q</script> heads, which  are used for returning different estimations of the action <script type="math/tex"> Q </script> values. For each episode, the bootstrapped exploration policy selects a single head to play with during the episode. According to the selected head, only the relevant output <script type="math/tex"> Q </script> values are used. Using those <script type="math/tex"> Q </script> values, the exploration policy then selects the action for acting.</p>
<h3 id="storing-the-transitions">Storing the transitions</h3>
<p>For each transition, a Binomial mask is generated according to a predefined probability, and the number of output heads. The mask is a binary vector where each element holds a 0 for heads that shouldn't train on the specific transition, and 1 for heads that should use the transition for training. The mask is stored as part of the transition info in the replay buffer. </p>
<h3 id="training-the-network">Training the network</h3>
<p>First, sample a batch of transitions from the replay buffer. Run the current states through the network and get the current <script type="math/tex"> Q </script> value predictions for all the heads and all the actions. For each transition in the batch, and for each output head, if the transition mask is 1 - change the targets of the played action to <script type="math/tex">y_t</script>, according to the standard DQN update rule:</p>
<p>
<script type="math/tex; mode=display"> y_t=r(s_t,a_t )+\gamma\cdot max_a Q(s_{t+1},a) </script>
</p>
<p>Otherwise, leave it intact so that the transition does not affect the learning of this head. Then, train the online network according to the calculated targets.</p>
<p>As in DQN, once in every few thousand steps, copy the weights from the online network to the target network.</p>
              
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